# no 4 on a plane (3*3*3 puzzle)

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### Torsten Sillke

Nov 27, 1992, 10:25:17 AM11/27/92
to
On the 2*2*2 grid you can take 5 points, such that no 4 points lay on a
plane. The only possibility (up to symmetry) is:

o . . o
o o o .

Can you find the only possibility to take 8 points in the 3*3*3 grid
with the same property?

good luck, Torsten Sillke
(as nobody mastered any of the puzzles I posted so far, I hope this is
easy enough for you.)

### Torben AEgidius Mogensen

Nov 27, 1992, 11:16:06 AM11/27/92
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sil...@math25.mathematik.uni-bielefeld.de (Torsten Sillke) writes:

>On the 2*2*2 grid you can take 5 points, such that no 4 points lay on a
>plane. The only possibility (up to symmetry) is:

> o . . o
> o o o .

>Can you find the only possibility to take 8 points in the 3*3*3 grid
>with the same property?

. o . o . . . . o
. . o . . . o . .
o . . . . o . o .

Torben Mogensen (tor...@diku.dk)

### der Mouse

Nov 28, 1992, 3:28:47 AM11/28/92
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In article <1992Nov27....@odin.diku.dk>, tor...@diku.dk (Torben AEgidius Mogensen) writes:
> sil...@math25.mathematik.uni-bielefeld.de (Torsten Sillke) writes:
>> On the 2*2*2 grid you can take 5 points, such that no 4 points lay
>> on a plane. [...] Can you find the only possibility to take 8

>> points in the 3*3*3 grid with the same property?

> . x . x . . . . o
> . . x . . . x . .
> o . . . . x . x .

Sorry. The six (!) points I marked with x are all in the same plane.

der Mouse

### David Seal

Nov 30, 1992, 10:31:11 AM11/30/92
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In article <1992Nov27....@odin.diku.dk> tor...@diku.dk (Torben
AEgidius Mogensen) writes:

>sil...@math25.mathematik.uni-bielefeld.de (Torsten Sillke) writes:
>>Can you find the only possibility to take 8 points in the 3*3*3 grid
>>with the same property?
>
>
>. o . o . . . . o
>. . o . . . o . .
>o . . . . o . o .

No, there's a diagonal plane which passes through no less than 6 of these
points!

. O . O . . . . o
. . O . . . O . .
o . . . . O . O .

The six points marked with upper-case "O"s are coplanar.

David Seal
ds...@armltd.co.uk

All opinions are mine only...

### helge_...@yahoo.de

Apr 5, 2016, 1:57:21 PM4/5/16
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Am Freitag, 27. November 1992 16:25:17 UTC+1 schrieb Torsten Sillke:
Let's take this one:

. o . . . . . . o
. o . o . . o . .
o . . . o o . . .

### henh...@gmail.com

Apr 6, 2016, 6:28:38 PM4/6/16
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Nice problem. Congratulations!

the American usage of [lie] & [lay] !

HH

### James Dow Allen

Apr 11, 2016, 1:30:15 AM4/11/16
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On Friday, November 27, 1992 at 10:25:17 PM UTC+7, Torsten Sillke wrote:
> On the 2*2*2 grid you can take 5 points, such that no 4 points lay on a
> plane....

By coincidence(?) this is the current problem ("Non-Coplanar Points")
being attacked at Al Zimmerman's Programming Contest:
http://azspcs.net/

Not for the faint of heart. 3x3x3 seems hard enough, but the
Contest requires an answer for 97x97x97.

James Dow Allen